A Closer Look at the Diffusion Equation


Series: Mathematics Research Developments
BISAC: MAT007020

Diffusion is a principle transport mechanism emerging widely at different scale, from nano to micro and macro levels. This is a contributed book of seventh chapters encompassing local and no-local diffusion phenomena modelled with integer-order (local) and non-local operators. This book collates research results developed by scientists from different countries but with common research interest in modelling of diffusion problems. The results reported encompass diffusion problems related to efficient numerical modelling, hypersonic flows, approximate analytical solutions of solvent diffusion in polymers and wetting of soils. Some chapters are devoted to fractional diffusion problem with operators with singular and non-singular memory kernels.

The book content cannot present the entire rich area of problems related to modelling of diffusion phenomena but allow seeing some new trends and approaches in the modelling technologies. In this context, the fractional models with singular and non-singular kernels the numerical methods and the development of the integration techniques related to the integral-balance approach form fresh fluxes of ideas to this classical engineering area of research.

The book is oriented to researchers; master and PhD students involved in diffusion problems with a variety of application and could serves as a rich reference source and a collection of texts provoking new ideas.

Table of Contents

Table of Contents


Chapter 1. A Numerical Approach to Solving Unsteady One-Dimensional Nonlinear Diffusion Equations
(István Faragó, Stefan M. Filipov, Ana Avdzhieva and Gabriella Svantnerné Sebestyén, Department of Differential Equations, Institute of Mathematics, Budapest University of Technology and Economics, Budapest, Hungary, and others)

Chapter 2. Diffusion in Hypersonic Flows
(H. Berk Gür and Sinan Eyi, PhD, Department of Aerospace Engineering, Middle East Technical University, Ankara, Turkey)

Chapter 3. On the Nonlinear Diffusion with Exponential Concentration-Dependent Diffusivity: Integral-Balance Solutions and Analyzes
(Jordan Hristov, Department of Chemical Engineering, University of Chemical Technology and Metallurgy, Soa, Bulgaria)

Chapter 4. Solutions for Fractional Reaction-Diffusion Equations
(D. Marin, L. M. S. Guilherme, M. K. Lenzi, E. K. Lenzi and P. M. Ndiaye, Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa, Paraná, Brazil, and others)

Chapter 5. Semi-analytical Solution of Hristov Diffusion Equation with Source
(Derya Avcı and Beyza Billur İskender Eroğlu, Department of Mathematics, Faculty of Sciences and Arts, Balikesir University, Balikesir, Turkey)

Chapter 6. Non-Gaussian Diffusion Emergence in Superstatistics
(Maike A. F. dos Santos, Department of Physics, Pontifical Catholic University, Rua Marquês de São Vicente, Gávea, Rio de Janeiro, Brazil, and others)

Chapter 7. Mean Square Displacement of the Fractional Diffusion Equation Described by Caputo Generalized Fractional Derivative
(Ndolane Sene, Laboratoire Lmdan, Département de Mathématiques de la Décision, Université Cheikh Anta Diop de Dakar, Faculté des Sciences Economiques et Gestion, Dakar Fann, Senegal)


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